What should I do with pigeon eggs?

I hate pigeons, I hate pigeons, I hate pigeons! Today I kept hearing pigeons outside of my bedroom window. Now this is strange because it's covered in netting to prevent pigeons from entering. I look outside my window, and low and behold, the little rascals found a way into my covered balcony. I shooed them away. A few hours later I heard them again. So this time when I went outside, but the pigeons weren't afraid, they just kind of hung in midair watching me. AAAHHH The Birds!! I got scared, so I grabbed the first thing I saw, a bike pump, stuck one arm outside the house and shook it furiously at them. They finally flew away after almost flying in my apartment, and that's when I saw it, DUN DUN DUN! A NEST!! They built a nest on my balcony AND it has TWO EGGS in it!!! I immediately went online to research pigeon removal while pondering: What should I do with these eggs? I have made a list of the possibilities:
1) Throw the eggs out in the trash. I don't know if this is the most humane thing to do.
2) Eat the eggs. Pigeon eggs are technically a food.
3) Let the baby pigeons grow, then eat them. My research confirmed that they taste like Cornish hens and are best eaten just before they leave the nest. In fact, they were once a popular food until chicken meat became more popular.
4) Let them grow, then make one of them my pet pigeon. I like this idea. I would call it Pete, Pete the Pigeon.
5) Put the nest outside somewhere and hope the parents find it. This might be the most rational idea.